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Properties

Label 3900.2.cp
Level $3900$
Weight $2$
Character orbit 3900.cp
Rep. character $\chi_{3900}(1379,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $2880$
Sturm bound $1680$

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Defining parameters

Level: \( N \) \(=\) \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3900.cp (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 300 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(1680\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3900, [\chi])\).

Total New Old
Modular forms 3392 2880 512
Cusp forms 3328 2880 448
Eisenstein series 64 0 64

Trace form

\( 2880 q + O(q^{10}) \) \( 2880 q - 4 q^{10} - 12 q^{16} + 28 q^{24} + 8 q^{25} + 34 q^{30} + 32 q^{34} + 60 q^{36} + 20 q^{40} + 100 q^{42} + 24 q^{45} + 2896 q^{49} - 6 q^{60} - 90 q^{66} + 48 q^{69} - 32 q^{70} + 96 q^{76} - 16 q^{85} + 82 q^{90} - 64 q^{94} - 76 q^{96} + 200 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3900, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(3900, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(3900, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(300, [\chi])\)\(^{\oplus 2}\)